In an interview in April, Robert Bigelow said he hopeful that the inflatable habitat his space company had developed would, in fact, inflate once it reached the International Space Station. But after SpaceX’s Falcon 9 rocket blew up last year, the launch of the habitat was delayed significantly.

“This has been waiting for a year," said Bigelow, the founder of Bigelow Aerospace. "We’ve didn’t expect that. We thought, well maybe three or four months. But it’s been cinched up really tight in that mode for over a year. We’re not necessarily concerned. It’s just one more element that we would rather not have. We’d like to have not gone through that. We don’t know if t it makes a different if it's cinched up for one year or ten years.”

Then, on Thursday, the big day came—the moment astronauts aboard the station would begin pumping air into the habitat, known as the BEAM, the Bigelow Expandable Activity Module.

It didn’t go so well.

The pressure was off, and after two and a half hours, NASA officials called it off for another day. Finally, on Saturday, the BEAM inflated successfully, giving the station another room.

This is how Raymond Z. Gallun, Golden Age master of science fiction, described the inflation of a space craft in 1961 (from The Planet Strappers:

Just then the order came, maddeningly calm and hard above the other sounds in Frank's phone: "All novices disembarked from GOs-11 and -12 must clear four-hundred mile take-off orbital zone for other traffic within two hours."

At once Frank was furiously busy, working the darkened stellene of his bubb from the drum, letting it spread like a long wisp of silvery cobweb against the stars, letting it inflate from the air-flasks to a firm and beautiful circle, attaching the rigging, the fine, radial spokewires—for which the blastoff drum itself now formed the hub. To the latter he now attached his full-size, sun-powered ionic motor. Then he crept through the double sealing flaps of the airlock, to install the air-restorer and the moisture-reclaimer in the circular, tunnel-like interior that would now be his habitation.
(Read more about space bubbles [bubbs])

Gallun's space bubbles were made of stellene, which has its own safety features, rather than layers of fabric with spacing between layers and an internal restraint and bladder system.

Also, take a look at the Inflatable Expansion Bubble from Crashlander (1994), by Larry Niven; this article contains more information about famed aerospace engineer Werner von Braun's inflatable space station idea from 1952.